Sanja Cvijić

Security constrained unit commitment and economic dispatch through benders decomposition: A comparative study

Security Constrained Unit Commitment (SCUC) is a complex optimization algorithm used for day-ahead planning in restructured electricity markets. There are many existing approaches for implementing SCUC, but this paper will focus on the ones based on General Benders Decomposition (GBD). GBD decomposes the SCUC problem into a master problem, feasibility checks and subproblems. This paper will give a comparison study of different ways how the SCUC problem can be decomposed using variations of the existing GBD framework. Our goal is to show all these possible mappings and determine properties of the algorithms in terms of solution quality and runtime scalability. IEEE test cases will be used to present behavior of the algorithms when applied to networks of different size.

Part I: A New Framework for Modeling and Tracing of Bilateral Transactions and the Corresponding Loop Flows in Multi-Control Area Power Networks

This paper introduces a novel multi-control area framework for explicit modeling, managing, and accounting of simultaneous bilateral transactions with specified contract paths. Our framework provides a modular and multi-layered electrical network representation with zooming-in and zooming-out capabilities. The zoomed-out representation concerns interconnections and inter-area transactions, while the zoomed-in representation concerns a single area and its internal transactions. The framework allows explicit modeling of bilateral transactions with contract paths through a transformation of a meshed electrical network into a spanning tree. Loop flows are introduced to represent a deviation between the contract paths of bilateral transactions and physical line flows. The effects of both intra-area and inter-area bilateral transactions and loop flows can be graphically traced in the framework. Moreover, these tracing methods allocate bilateral transactions to line flows and loop flows, essential for accounting and flow control. Our tracing methods differ from the distribution factor based method because the distribution factor matrix handles nodal injections only and it cannot account for contract paths of bilateral transactions and the resulting loop flows. The multi-layered network transformations and tracing methods are illustrated on the IEEE 14-bus system.

Optimal clustering for efficient computations of contingency effects in large regional power systems

The goal of this paper is to determine optimal clustering in large power networks for efficient contingency screening. A decentralized algorithm for “DC” contingency screening based on Diakoptics is revisited first. It has been shown that this algorithm is much more computationally efficient compared to the existing Distribution Factor Matrix methods for a pre-specified clustering. This paper will address how to establish the best clustering and quantify how much more efficient that clustering is compared to a pre-specified one. The optimality is defined in terms of computational complexity and necessary communication among the clusters. The optimal clustering requires the minimum balanced computational effort across the clusters with the minimum amount of information exchange. Optimal clustering will be illustrated on a sparsely connected RTS-96 bus system and a densely connected NPCC 36-bus system.

Applications of Homotopy for solving AC Power Flow and AC Optimal Power Flow

This paper introduces a new paradigm for solving AC Power Flow (ACPF) and AC Optimal Power Flow (ACOPF) with improved convergence robustness. This approach exploits the globally convergent properties of continuation methods. Continuation methods achieve robustness by generating a sequence of nonlinear problems and repeatedly and consistently providing good initial guesses for locally convergent nonlinear solvers such as Newton-Raphson. The Homotopy implemented in this paper, (referred to as Power Flow Homotopy, PFH), is formulated in a way that gradually transforms the “easy” DC into the “difficult” AC Power Flow. Successive changes of the homotopy parameter modify the system of equations from fully linear and convex DC into non-linear and non-convex AC (optimal) power flow. As a result, the AC solution is obtained with increased robustness and multiple AC power flow solutions can also be detected. Similarly, Optimal Power Flow Homotopy (OPFH) is defined for solving AC Optimal Power Flow, by gradually transforming the convex DC OPF problem. Simulation results provide a comparison between the simple Newton-Raphson method and PFH in terms of performance and quality of detected solution. Comparisons are also performed between the Interior-Point method and OPFH.

A graph-theoretic approach to modeling network effects of phase shifters on active power loop flows

This paper proposes a new method for modeling effects of phase shifters in “DC” electric power networks. The new model, based on the diakoptics algorithm, provides intuitive graph-theoretic insights on how phase shifters affect real power line flows. The effect of a phase shifter is modeled with loop flows in every basic loop of a meshed graph representing an electric power system. The model can be used to analyze the active power line flows as the superposition of the loop flows caused by a phase shifter and the loop flows created by power injections. Compared to the conventional distribution matrix-based approach, this method provides a straightforward interpretation of power flow redistribution by means of phase shifters. The new modeling technique is illustrated on an example along with a potential application for loop flow reduction.

On limits to the graph-theoretic approaches in the electric power systems

There have been numerous attempts to use graph-theoretic algorithms in power systems. But it has not been clear enough what the potentials and the limitations of these applications are. The goal of our work is to model differences between transportation and electrical networks and to provide a uniform way for transforming an electrical network into its transportation equivalent. The limitations of the application of graph algorithms are discussed based on this transformation. After obtaining a transportation equivalent of an electrical network, two famous graph algorithms: Max-Flow and Min-Cost Flow are executed in a tree representation.

Operating beyond today's PV curves: Challenges and potential benefits

Accounting for system-level voltage-related operating problems represents a rather complex challenge. We first suggest that todays practice based on the use of PV curves in large power grids neither guarantees feasible power transfer nor enables the most economic utilization of real power. To overcome this problem, the use of a full-blown AC Optimal Power Flow (AC OPF) to support utilization and delivery of real power is proposed. This leads to a combined adjusting of real power generation and voltage generator settings of the Automatic Voltage Regulators (AVRs) and T&D voltage-controllable equipment such as on-load tap changing transformers (OLTCs) and shunt capacitor banks. We illustrate the proposed approach on the small IEEE 14 bus power system and on large ERCOT and PJM systems. We present a comparison of todays PV-curve-based management of voltage-related delivery problems and the proposed full-blown AC OPF.

Area-level reduction of wheeling loop flows in regional power networks

This paper introduces a new framework for modeling wheeling loop flows across areas not directly involved in bilateral trades. This framework decomposes each wheeling loop flow into a linear combination of contributions by the individual bilateral trades. It has zooming-in and zooming-out capabilities for modeling the level of details of interest. The zoomed-in network representations neglect interconnections while treating areas fully disconnected from the rest of the network. This feature allows to have distributed algorithms with completely decentralized decision making. In this framework, we formulate distributed algorithms for wheeling loop flow reduction which do not require individual areas to reveal their internal generation and load. Loop flow minimization is achieved by rescheduling generation within areas directly involved in bilateral trades. Since this rescheduling leads to a more expensive economic dispatch, we define a new Optimal Power Flow (OPF) problem that accounts for wheeling charges and generation cost. Simulation results are illustrated on the IEEE 14-bus system and the RTS 96-bus system.

Optimal voltage management for enhancing electricity market efficiency

In this paper we propose to schedule both real power and voltage settings of generators participating in electricity markets. This can be done by utilizing an extended AC Optimal Power Flow (AC X-OPF). This will provide a one-step method performed by the Independent System Operator (ISO) in charge of electricity market clearing; iterative decisions by the ISO and the system operator ultimately responsible for reliable operation can be significantly reduced. Moreover, the locational marginal prices (LMPs) are straightforward to interpret, as these are the nodal prices based on physically deliverable bid clearing. It is shown using the PJM system that the economic gains are significant. In addition to reducing total generation cost, LMPs are much less volatile and always positive. Overall, optimizing generation voltages leads to a much better behaving and more efficient electricity market.

Part II: PAR Flow Control Based on the Framework for Modeling and Tracing of Bilateral Transactions and Corresponding Loop Flows

This paper defines flow control algorithms for loop flow cancellation based on the allocation and tracing of bilateral transactions and loop flows. In Part I of this paper, we have shown that the main difference between transportation and electrical networks is caused by the existence of loop flows. We have introduced a distributed framework for the modeling and tracing of bilateral transactions and the corresponding loop flows. Its zooming-out capability provides a valuable mechanism for representing external (inter-area) loop flows based on simplified topologies of individual areas. The tracing information accurately allocates bilateral transactions with associated contract paths to line flows and loop flows. Furthermore, this information can be used for determining the set points of control equipment so that loop flows are minimized. In this framework, phase angle regulators (PARs), commonly used for line flow control, are represented through their effects on loop flows. We define sufficient conditions for achieving complete loop flow cancellation. A new distributed algorithm for determining PAR set points in a coordinated way without revealing operating conditions of individual areas is introduced in this part. Finally, complete loop flow cancellation and the distributed algorithm for finding PAR set points are demonstrated in the Reliability Test System (RTS) 96-bus system with wheeling loop flows.